Edge-state transport in gapped bilayer graphene

Abstract

We investigate electronic transport in gapped bilayer graphene (gBLG) devices. For certain edge terminations -typically a combination of zigzag, armchair, and bearded types - we observe edge state conduction within the band gap, which is opened by a potential bias between the two layers. The edge states can generate a non-local resistance, in line with recent experiments [1]. Band structure calculations of gBLG nanoribbons corroborate the existence of the edge states, whose edge localization can be switched by tuning the electron energy. Their existence strongly depends on the edge termination and does not originate from a topological bulk-boundary correspondence.

Figures (7)

• Figure 1: Squematic of the gBLG devices. A 'cookie cutter', defined by the vectors $\mathbf{T}_1$ and $\mathbf{T}_2$, is rotated by the angle $\phi$ above an AB stacked BLG lattice. The colored regions correspond to the source contact $S$ (green), and three drain contacts $D_L$ (blue), $D_M$ (yellow) and $D_R$(red).
• Figure 2: Conductance $\mathcal{G}$ between the source $S$ and three drain contacts $D_{L/M/R}$ in gBLG devices as a function of the edge orientation $\phi$ and electron energy $E$. The energy gap is easily identified in $\mathcal{G}_{SD_M}$ because electronic transport is suppressed inside the energy range $[-\frac{\epsilon_g}{2},\frac{\epsilon_g}{2}]$ (black horizontal lines). The transport signals within the gap, which are present in both, $\mathcal{G}_{SD_L}$ and $\mathcal{G}_{SD_R}$, but absent in $\mathcal{G}_{SD_M}$, suggest edge transport.
• Figure 3: Current density, indicated by the red color shading, for electrons with energy $E$ in gBLG devices with different edge orientations $\phi$. All panels prove that transport in the gap takes place at the edges of the devices. Panels (a-d) are for devices with size $28.4 \times 35.5\,\mathrm{nm}$, which are used also for the calculations of the conductance and non-local resistance. In panels (e-h) the size of the device is increased to $69.6 \times 79.5 \,\mathrm{nm}$, but the parameters are otherwise the same to demonstrate that the edge states are rather size independent. The current flow can be localized at both edges (a,c,e,g) or only at a single one (b,d,f,h). Importantly, this edge localization of the current can even be switched by the electron energy (b-c,g-f).
• Figure 4: Non-local resistance $R_{\text{NL}}$ as a function of edge orientation $\phi$ and energy $E$. A setup with 4 contacts at the corners of the device is used and two distinct contact wirings are studied. Clear signals of $R_\text{NL}$ are found within the band gap due to edge transport. Exceedingly large values of $R_{NL}$ (gray regions) are due to a negligible current between $S$ and $D$.
• Figure 5: gBLG nanoribbon construction. Superlattice vectors $\mathbf{t}_1$ and $\mathbf{t}_2$ define the unit cell of the nanoribbon. The edge of the nanoribbon is along the periodic direction $\mathbf{t}_2$ and the finite width is $3\mathbf{t}_1$. The angle $\phi'$ links a given nanoribbon to a device with edge orientation $\phi$. The edges of the nanoribbon are modified by the parameters $\Delta_1, \Delta_2$ and $\Delta_3$.